Gas turbine engines generally include a compressor, such as an axial compressor, to pressurize inflowing air. Axial compressors may include number of rotor segments adjacent and coupled to each other in the axial direction. As the compressor operates, air temperature increases along the rotors in the aft direction. Cooling of the inner rim may tend to prevent fatigue and potentially extend the life of the material of the rims. Directed and/or bleeding cooler air to the inner rim may improve performance and extend the life of the inner rim.